Section C Section C Checkpoint

Problem 1

Select all the expressions that can give the value of

6 \div \frac{3}{2}

6 \boldcdot \frac{3}{2}

(6 \boldcdot 2) \div 3

(6 \div \frac{1}{2}) \div 3

6 \boldcdot 2 \boldcdot \frac{1}{3}

(6 \div 2) \div 3

6 \boldcdot \frac{2}{3}

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Solution

B, C, D, F

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Sample Response

B, C, D, F

Calculate each quotient. Show your reasoning.

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Solution

$\frac{3}{4}$ (or equivalent). Sample reasoning:
- $\frac{9}{8} \div \frac{3}{2} = \frac{9}{8} \boldcdot \frac{2}{3} = \frac{18}{24} = \frac{3}{4}$
- The quotient is the unknown factor in the multiplication equation $\frac{3}{2} \boldcdot {?} = \frac{9}{8}$ . That number is $\frac{3}{4}$ .
$\frac{21}{2}$ or $10\frac{1}{2}$ (or equivalent). Sample reasoning:
- $\frac{21}{10} \div \frac{1}{5} = \frac{21}{10} \boldcdot 5 = \frac{105}{10} = 10\frac{5}{10}$
- There are 10 groups of $\frac{1}{5}$ in 2 wholes, and $\frac{1}{10}$ is $\frac{1}{2}$ a group of $\frac{1}{5}$ , so there are $10\frac{1}{2}$ groups of $\frac{1}{5}$ in $2\frac{1}{10}$ .

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Sample Response

$\frac{3}{4}$ (or equivalent). Sample reasoning:
- $\frac{9}{8} \div \frac{3}{2} = \frac{9}{8} \boldcdot \frac{2}{3} = \frac{18}{24} = \frac{3}{4}$
- The quotient is the unknown factor in the multiplication equation $\frac{3}{2} \boldcdot {?} = \frac{9}{8}$ . That number is $\frac{3}{4}$ .
$\frac{21}{2}$ or $10\frac{1}{2}$ (or equivalent). Sample reasoning:
- $\frac{21}{10} \div \frac{1}{5} = \frac{21}{10} \boldcdot 5 = \frac{105}{10} = 10\frac{5}{10}$
- There are 10 groups of $\frac{1}{5}$ in 2 wholes, and $\frac{1}{10}$ is $\frac{1}{2}$ a group of $\frac{1}{5}$ , so there are $10\frac{1}{2}$ groups of $\frac{1}{5}$ in $2\frac{1}{10}$ .